This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A261359 #48 Oct 31 2015 15:32:04
%S A261359 1,1,1,2,2,1,2,4,4,1,4,4,4,8,4,1,3,6,6,3,12,12,12,24,12,1,6,6,12,24,
%T A261359 12,8,24,24,8,1,4,8,8,6,24,24,24,48,24,4,24,24,48,96,48,32,96,96,32,1,
%U A261359 8,8,24,48,24,32,96,96,32,16,64,96,64,16,1,5,10,10,10,40,40,40,80,40,10,60,60,120,240,120,80,240,240,80,5,40,40,120,240,120,160,480,480,160,80,320,480,320,80,1,10,10,40,80,40,80,240,240,80,80,320,480,320,80,32,160,320,320,160,32
%N A261359 Pentatope of coefficients in expansion of (1 + x + 2*y + 2*z)^n.
%C A261359 T(n,i,j,k) is the number of lattice paths from (0,0,0,0) to (n,i,j,k) with steps (1,0,0,0), (1,1,0,0) and two kinds of steps (1,1,1,0) and (1,1,1,1).
%C A261359 The sum of the numbers in each cell of the pentatope is 6^n (A000400).
%F A261359 T(i+1,j,k,l) = 2*T(i,j-1,k-1,l-1) + 2*T(i,j-1,k-1,l) + T(i,j-1,k,l) + T(i,j,k,l); T(i,j,k,-1)=0,...; T(0,0,0,0)=1.
%F A261359 T(n,i,j,k) = 2^j*binomial(n,i)*binomial(i,j)*binomial(j,k). - _Dimitri Boscainos_, Aug 21 2015
%e A261359 The 5th slice (n=4) of this 4D simplex starts at a(35). It comprises a 3D tetrahedron of 35 terms whose sum is 1296. It is organized as follows:
%e A261359 .
%e A261359 . 1
%e A261359 .
%e A261359 . 4
%e A261359 . 8 8
%e A261359 .
%e A261359 . 6
%e A261359 . 24 24
%e A261359 . 24 48 24
%e A261359 .
%e A261359 . 4
%e A261359 . 24 24
%e A261359 . 48 96 48
%e A261359 . 32 96 96 32
%e A261359 .
%e A261359 . 1
%e A261359 . 8 8
%e A261359 . 24 48 24
%e A261359 . 32 96 96 32
%e A261359 . 16 64 96 64 16
%p A261359 p:= proc(i, j, k, l) option remember;
%p A261359 if l<0 or j<0 or i<0 or i>l or j>i or k<0 or k>j then 0
%p A261359 elif {i, j, k, l}={0} then 1
%p A261359 else p(i, j, k, l-1) +p(i-1, j, k, l-1) +2*p(i-1, j-1, k, l-1)+2*p(i-1, j-1, k-1, l-1)
%p A261359 fi
%p A261359 end:
%p A261359 seq(seq(seq(seq(p(i, j, k, l), k=0..j), j=0..i), i=0..l), l=0..5);
%p A261359 # Adapted from _Alois P. Heinz_'s Maple program for A261356
%o A261359 (PARI) lista(nn) = {for (n=0, nn, for (i=0, n, for (j=0, i, for (k=0, j, print1(2^j*binomial(n,i)*binomial(i,j)*binomial(j,k), ", ")););););} \\ _Michel Marcus_, Oct 07 2015
%Y A261359 Cf. A000400, A189225, A261358, A261360.
%K A261359 nonn,tabf,walk,less
%O A261359 0,4
%A A261359 _Dimitri Boscainos_, Aug 16 2015